The 57-year-old Bhattacharya, the front-runner for the post on account of years of service left, was managing director and chief financial officer of the bank prior to her elevation.
An SBI statement this evening said Bhattacharya assumed charge as the chairperson of the bank today, succeeding Pratip Chaudhuri who retired on September 30.
SBI, which has a chairman/chairperson unlike other Public Sector Banks (PSBs) who have a combined post of CMD, has four MDs. Bhattacharya's elevation leaves one MD post vacant.
It also has over a dozen Deputy MDs and over 35 Chief General Managers (CGMs).
Bhattacharya joined SBI as a probationary officer in 1977 and has had stints in areas such as retail, treasury and corporate finance during her 36-year career.
She has held various positions including Deputy Managing Director and Corporate Development Officer, Chief General Manager of the Bangalore circle and new businesses and head of its merchant banking arm, SBI Caps, the statement said.
Bhattacharya also played an important role in setting up general insurance, custody services and SBI Macquarie Infrastructure Fund subsidiaries, the statement added.
She also had a stint at the bank's New York office as the head of external audit and correspondent relations, SBI said.
Her appointment comes at a time when the government is all set to open the country's first bank dedicated for women, Bhartiya Mahila Bank.
Bhattacharya joins other women heading public sector banks -- Allahabad Bank (Shubhalakshmi Panse) and Bank of India (VR Iyer) and private sector banks -- Chanda Kochhar of ICICI Bank, Shikha Sharma of Axis Bank and Naina Lal Kidwai of HSBC India.
SBI and its five subsidiaries today control over one-fifth of the nation's banking assets and is the 66th largest bank in the world.
SBI traces its roots to the British era when the English set up Bank of Calcutta in 1806, to be followed by Bank of Bombay in 1840 and Bank of Madras in 1843.
In 1921, the British merged all these three banks to form the Imperial Bank of India, based in Calcutta and in 1955, the Nehru government nationalised the Imperial Bank and renamed it as the State Bank of India through an Act of Parliament.